To make the butternut squash: Preheat the oven to 400ºF. Heat a large ovenproof skillet over high heat and add the butter and the olive oil. When the butter foams, add the squash and cook, shaking the pan occasionally, until caramelized and lightly browned, about 3 minutes. Slide the pan into the oven and roast until a deeper brown on the edges, about 20 minutes.

To make the vinaigrette: Heat a small sauté pan over medium heat, add the butter, and when it foams, brown the sage for just a minute, and then pour in the vinegar and let it reduce by half. Don’t stir or touch it. Just keep it at a simmer, gently reducing until thickened. When it’s the consistency of a light syrup, add the salt. Turn off the heat but leave the pan on the stove while you sauté the mushrooms.

To make the mushrooms: Heat a medium sauté pan or skillet over medium-high heat and add 2 tablespoons butter and olive oil. When the butter foams, add the mushrooms and sauté until they begin to release their water, about 8 minutes. Add the shallots to the pan and sauté until brown, 3 to 4 minutes, tossing so they cook evenly. Season with salt and pepper and add another ½ tablespoon of butter if they look dry.

Divide the squash and the mushrooms evenly among 6 plates. Tear the burrata into pieces, scattering them over the vegetables. Drizzle with the vinaigrette. Serves 6.

To make the gravy: Preheat the oven to 425°F. Remove necks and giblets and put into a large saucepan. Add onions, 2 carrots, 2 celery stalks, and the chicken stock. Bring to a boil over high heat and then reduce the heat and let simmer until reduced to about 2 cups. Strain and reserve; this is the turkey stock that you will use for the gravy.

To make the brine: Combine all brine ingredients (except for ice) in a stockpot, and bring to a boil. Stir to dissolve solids, then remove from heat, add ice and cool to room temperature. Refrigerate until thoroughly chilled.

Wash turkeys and place in brine, cover, then refrigerate overnight, about 12 hours. Turn turkeys once, halfway through brining.

Remove turkeys from brine and pat dry. Coat both inside and out with olive oil. Season each turkey on the outside generously with the spice rub, pressing it in to adhere.

Arrange 2 of the halved carrots and 4 celery stalks on 2 half-sheet pans or baking sheets. Position each turkey on top of the carrots and celery so that the turkey does not rest directly on the bottom of the pan. Drizzle turkeys with remaining olive oil.

Roast until an instant-read thermometer (inserted deep into the thigh but away from the bone) reads 165°F and juices in the thigh run clear when pierced with a fork, about 2 to 2 1/2 hours; begin checking at 2 hours. Remove from the pans and let rest for 15 minutes before carving. Reserve pan juices for gravy.

While turkeys are resting, make the gravy. In a medium heavy saucepan, cook flour and butter over medium heat for 3 to 4 minutes, or until a blond roux is formed. Add pan juices and then reserved turkey stock and bring to a boil over high heat. Reduce the heat and let simmer until thickened and ready to serve.

Put the fennel seeds, coriander seeds and peppercorns in a heavy pan over medium heat. Watch carefully, tossing frequently so the seeds toast evenly. When light brown and fragrant, pour the seeds onto a plate to cool. They must be cool before grinding, or they will gum up the blades.

Pour the seeds into a blender and add the salt. Blend to a fine powder, shaking the blender occasionally to redistribute the seeds. Store in a tightly sealed glass jar in a cool, dry place, or freeze. Makes 1½ cups.

Tip: Use lots of the seasoning because half of it will fall off during the cooking process.

Preheat the oven to 350°F. Spread the panettone cubes out on two rimmed baking sheets. In a small saucepan, melt 2 tablespoons of the butter over medium heat and cook until light brown, about 6 minutes. Remove from the heat and add half the sage. Season with salt and pepper. Pour the sage butter over the bread and toss gently but swiftly. Toast the bread in the oven, turning with a spatula halfway through cooking, until light brown, about 15 minutes. Remove from the oven and pour the croutons into bowl, leaving the oven on.Meanwhile, put the dried fruit in a large bowl and add boiling water to cover. Let soak for at least 10 minutes to make the fruit plump and soft. Drain and set aside.

Increase the oven temperature to 375°F. Heat a large sauté pan or skillet over medium-low heat, add the remaining 2 tablespoons butter, and cook until it foams. Add the onion, celery, and carrot and sauté until soft, 12 to 15 minutes. Stir in the plumped fruit and remaining sage, then add to the cooled croutons and gently toss. Add the 1 ½ cups stock to moisten. Add more stock if you like a softer stuffing. For a firmer stuffing, stir in the beaten egg now. Taste and adjust the seasoning.

Put the stuffing in a baking pan and cook, covered, at 375°F for about 30 minutes. Uncover and cook until browned at the top, approximately another 10 minutes.

In a pot large enough to hold your branch sections, bring salted water to a boil. Gently lower the sections into the water and cook for 2 to 3 minutes, or just until a Brussels sprout is crisp-tender (drop any heads that have come loose into the water and use those as your test subjects to decide when the branch is ready). Carefully remove the sections from the water and set them aside.

Preheat the oven to 425ºF. In a small saucepan, melt the butter over high heat and cook for 1 minute until it just begins to turn brown. Stir in the spice blend and remove from the heat. Put the branch sections in a roasting pan or a rimmed baking sheet and drizzle the butter mixture over them. Slide the pan into the oven and roast until the outer leaves of the heads just begin to show some browning, about 8 minutes. The outer leaves should be brown and crisp. Carefully transfer the sections to a platter. If you like, prop the sections into a typee for a dramatic presentation. Have guests snap the heads off the branch to add to their plates—or just pop in their mouths. Serves 8 to 10.

To make tart dough: Combine the flour, sugar and salt in a food processor and pulse to blend. Add the butter and pulse until the mixture forms coarse crumbs. Stir together the ¼ cup ice water and the vanilla; sprinkle the water over the mixture in the processor and pulse just until a dough forms, adding a little extra ice water if necessary.

Divide the dough in half, and shape each half into a 1-inch-thick round. Wrap 1 disk tightly in plastic wrap and refrigerate for at least 1 hour; freeze the other for a future use. Put a pizza stone in the oven and preheat the oven to 425ºF for 45 minutes. Remove the dough from the refrigerator about 15 minutes before rolling to soften it slightly.

Place the dough round between 2 sheets of parchment paper and roll into a 13-inch round, flouring the round lightly as needed to keep the dough from sticking. Remove the top sheet of parchment. Slide a pizza peel or rimless baking sheet under the bottom sheet of parchment.

To make the filling: Combine the apples, sugar, flour, and cinnamon in a bowl and toss well. Fill the center of the dough round with the apples in an even layer, leaving a border of about 1 ½ inches. Fold the border up and over the apples to make a rim. Brush the rim with egg wash, then sprinkle with coarse sugar. Trim the excess parchment with scissors.

Use the pizza peel or baking sheet to transfer the crostata, still with parchment underneath, to the oven, sliding it, with the paper, directly onto the pizza stone. Bake until the crust is nicely browned and the apples are bubbling, about 40 minutes. Remove from the oven with the peel or baking sheet and let cool on a rack for 15 minutes before serving. Serve warm.